For the connection of pipe ends the use of socket fittings is known, whereby each has one part which is a smooth end and another one which is an overlapping socket with inserted sealing ring, said parts being inserted into each other. For this plug connection, relatively long, straight pipe ends are needed. Further, it is known to provide each pipe to be connected with a flange and to connect the pipes to each other by bolting them together at said flanges. This type of connection is cumbersome and because of the bolts an added pipe elbow often can not be fastened in the desired position. For the thread area of the bolts it is necessary to have on the pipe a straight end of sufficient length which raises the curvature at one side of the arch. As a consequence, in the setting of pipes with tight curvatures in the above-mentioned manner considerable difficulties arise. In practice, piping is set mostly along the masonry and in the case of wall projections, other obstacles or corners the piping has to avoid these in a space-saving and snug manner, which is not achievable in a sufficient degree with the fittings known up to now. In order to plot different curves with pipes having the same section up to now pipe fittings with constant arc length of 15.degree., 30.degree., 45.degree., 60.degree. and 90.degree. were developed coupling piece. With these many pipe elbows of different arc sizes the piping can be installed in a more advantageous manner along the wall, but due to the excessive variety of the pipe elbows a very high mounting support is needed. In spite of that it is still not possible to install piping with very sharply curved paths.